This is Chapter 5 of Figuring Fibers, edited by Carolyn Yackel and sarah-marie belcastro.

This self-contained chapter contains directions for a complete project in a downloadable PDF file. You may also purchase the entire volume or see a list of all chapters available for individual purchase.

Background for crafters:

In knitting stitch dictionaries, a stitch pattern is usually described as being a “multiple of \(m\) plus \(a\)”. We translate this into the notation of modular arithmetic as \(a\) mod \(m\). The Chinese Remainder Theorem gives a method for finding a number that is consistent with several stitch patterns simultaneously, allowing a knitter to combine different stitch patterns in one piece without changing the number of stitches. We describe this method and then go on to consider the much harder problem of how to adjust when the stitch patterns have different stitches per inch (spi) measurements. To demonstrate the basic use of the Chinese Remainder Theorem, we give a pattern for a striped cowl with three different stitch patterns.

About Figuring Fibers:

Pick up this book and dive into one of eight chapters relating mathematics to fiber arts! Amazing exposition transports any interested person on a mathematical exploration that is rigorous enough to capture the hearts of mathematicians. The zenith of creativity is achieved as readers are led to knit, crochet, quilt, or sew a project specifically designed to illuminate the mathematics through its physical realization. The beautiful finished pieces provide a visual understanding of the mathematics that can be shared with those who view them. If you love mathematics or fiber arts, this book is for you!